237 LearnersLast updated on May 26th, 2025
Divisibility Rule of 99
The divisibility rule is a way to find out whether a number is divisible by another number without using the division method. In real life, we can use the divisibility rule for quick math, dividing things evenly, and sorting things. In this topic, we will learn about the divisibility rule of 99.
What is the Divisibility Rule of 99?
The divisibility rule for 99 is a method by which we can find out if a number is divisible by 99 or not without using the division method. Check whether 297 is divisible by 99 with the divisibility rule.
Step 1: Check if the given number is divisible by both 9 and 11. First, check divisibility by 9: Add all the digits of the number. For 297, 2+9+7=18, which is divisible by 9.
Step 2: Next, check divisibility by 11: Alternately subtract and add the digits of the number. For 297, calculate 2-9+7=0, which is divisible by 11.
Step 3: Since 297 is divisible by both 9 and 11, it is divisible by 99.
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Tips and Tricks for Divisibility Rule of 99
Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 99.
- Know the multiples of 99: Memorize the multiples of 99 (99, 198, 297, 396...etc.) to quickly check the divisibility. If the result from the checks shows divisibility by both 9 and 11, then the number is divisible by 99.
- Use the divisibility rules for 9 and 11: Familiarize yourself with the divisibility rules for 9 (sum of digits is divisible by 9) and 11 (alternating sum of digits is divisible by 11) to make the process easier.
- Repeat the process for large numbers: Students should keep repeating the divisibility process for both 9 and 11 until they confirm divisibility by 99. For example, check if 594 is divisible by 99. 5+9+4=18 (divisible by 9), and 5-9+4=0 (divisible by 11). Hence, 594 is divisible by 99.
- Use the division method to verify: Students can use the division method as a way to verify and crosscheck their results. This will help them to verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 99
The divisibility rule of 99 helps us to quickly check if the given number is divisible by 99, but common mistakes like calculation errors lead to incorrect conclusions. Here we will understand some common mistakes that will help you to understand.
Mistake 1
Not checking both conditions.
Students should ensure they check divisibility by both 9 and 11. A number must meet both criteria to be divisible by 99.
Mistake 2
Miscalculating the alternating sum for 11.
Pay close attention to the order of subtraction and addition when calculating the alternating sum for 11.
Mistake 3
Not repeating the process for large numbers.
Students often stop the process after checking only once. The process should be repeated to ensure accuracy.
Mistake 4
Confusing the steps.
Students often confuse the steps or forget them. To avoid errors, students should practice regularly.
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Divisibility Rule of 99 Examples
Problem 1
Is 198 divisible by 99?
Yes, 198 is divisible by 99.
Explanation
To determine if 198 is divisible by 99:
1) Split the number into two parts: 1 and 98.
2) Add these parts together: 1 + 98 = 99.
3) Check if the result is a multiple of 99. Yes, 99 is a multiple of 99 (99 × 1 = 99).
Problem 2
Check the divisibility rule of 99 for 594.
Yes, 594 is divisible by 99.
Explanation
For checking the divisibility of 594:
1) Break it into two parts: 5 and 94.
2) Add these parts together: 5 + 94 = 99.
3) Verify if the sum is a multiple of 99. Yes, 99 is a multiple of 99 (99 × 1 = 99).
Problem 3
Is 297 divisible by 99?
Yes, 297 is divisible by 99.
Explanation
To check if 297 is divisible by 99:
1) Divide the number into two parts: 2 and 97.
2) Add the two parts: 2 + 97 = 99.
3) Confirm if the sum is a multiple of 99. Yes, 99 is a multiple of 99 (99 × 1 = 99).
Problem 4
Can 450 be divisible by 99 following the divisibility rule?
No, 450 isn't divisible by 99.
Explanation
To verify if 450 is divisible by 99:
1) Separate the number into two parts: 4 and 50.
2) Add the parts together: 4 + 50 = 54.
3) Check if the result is a multiple of 99. No, 54 isn't a multiple of 99.
Problem 5
Check the divisibility rule of 99 for 891.
Yes, 891 is divisible by 99.
Explanation
To determine if 891 is divisible by 99:
1) Split the number into two parts: 8 and 91.
2) Add the parts: 8 + 91 = 99.
3) Confirm if the sum is a multiple of 99. Yes, 99 is a multiple of 99 (99 × 1 = 99).
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FAQs on Divisibility Rule of 99
1.What is the divisibility rule for 99?
2.How many numbers are there between 1 and 500 that are divisible by 99?
3. Is 792 divisible by 99?
4.What if I get 0 in the alternating sum for 11?
5.Does the divisibility rule of 99 apply to all integers?
6.How can children in United States use numbers in everyday life to understand Divisibility Rule of 99?
7.What are some fun ways kids in United States can practice Divisibility Rule of 99 with numbers?
8.What role do numbers and Divisibility Rule of 99 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Divisibility Rule of 99 skills?
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Important Glossaries for Divisibility Rule of 99
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not. For example, a number is divisible by 2 if it ends with an even number.
- Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 99 are 99, 198, 297, etc.
- Alternating sum: The process of alternately subtracting and adding digits of a number to determine divisibility by 11.
- Integer: A whole number that can be positive, negative, or zero.
- Verification: The process of confirming a result by using a different method, such as division, to ensure accuracy.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
